If sec A + tan A = 5,then sin A is equal to:

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SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 2)
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  1. \(\frac{5}{13}\)
  2. \(\frac{5}{12}\)
  3. \(\frac{13}{12}\)
  4. \(\frac{12}{13}\)

Answer (Detailed Solution Below)

Option 4 : \(\frac{12}{13}\)
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Detailed Solution

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Given:

sec A + tan A = 5

Concept used:

If sec A + tan A = x then,

⇒ sec A - tan A = 1/x

Formula used:

Sin θ = P/H ; sec θ = H/B ; tan θ = P/B

Pythagorean theorem:

 H2 = P2 + B2

Where, H = hypotenuse ; P = perpendicular ; B = base

Calculation:

⇒ sec A + tan A = 5 ------- (1)

then,

⇒ sec A - tan A = 1/5 -------- (2)

Adding the eq.(1) and (2)

⇒ Sec A + tan A + sec A - tan A = 5 + (1/5)

⇒ 2 × sec A = 26/5

⇒ sec A = 13/5 = H/B

By Pythagorean theorem:

⇒ H2 = P2 + B2

⇒ (13)2 = P2 + 52

⇒ P2 = 169 - 25 = 144

⇒ P = √144 = 12 

Sin A = P/H = 12/13

∴ The correct answer is 12/13.

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